Guided Inquiry – A Mathematical Perspective

As I completed the final day of my guided Inquiry training this past Fall, describing myself as anxious would’ve been a major understatement. Our Geometry team had created a Guided Inquiry Unit for our students to complete right after Winter Break, and I honestly no idea what to expect. As a teacher interested in engagement opportunities, I was thrilled. However, from a classroom management perspective, I was terrified. I had no idea what my students were going to study, what they were going to find interesting, or what type of project they were going to create. As Winter Break came a close, I crossed my fingers (and toes!), and began this new experience.

As a class, we dove into ratios and proportions head on, with a new interest in real world applications, or most commonly phrased as the “why do we care?!” factor. My students kept a journal they wrote in one to two times a week, and I was fascinated by their responses. Overwhelmingly, they were so appreciative of my change of teaching! They enjoyed knowing the “why” of things, and felt much more connected to this chapter than any other we had covered so far. I couldn’t believe what I was reading! They were truly interested in mathematics! Quickly, my anxiety was replaced with hope and pure joy.

For my student’s create phase, they were to research a topic of their choice, and create a presentation and model of something in the real world. Common topics chosen included baking, toys cars (such as hot wheels), and movie sets.

However, one of the most interesting projects created involved Sea World’s Shamu and the animal’s large tank. The group of students created a model tank that was proportional to Shamu’s real tank. They weighed their model, thanks to a lovely science teacher, and converted its weight to pounds. Then, using proportions, discovered how much water would need to be in the tank with this model to be proportional to the real tank at Sea World. My students were so engaged in finding the correct answer, I think for a time they forgot they were in math class. I sat in awe as they presented their work, overcome with joy that these students were indeed mine.

As the unit came to a close, all of my students completed one final journal reflecting on the chapter, giving feedback, and rating this unit from 1-10. As a whole, everyone loved the unit. Many students enjoyed the project aspect of the unit. Others loved the real world applications. Finally, the majority couldn’t thank me enough of allowing them to study something they truly had an interest in. As a teacher, I felt I had truly done something amazing in my classroom.

To all my math teachers out there who are afraid of Guided Inquiry, I was too. But, don’t let that fear stop you from allowing your students to create something great. I encourage you to give Guided Inquiry a try – I promise you won’t be disappointed! Don’t let anyone tell you Guided Inquiry isn’t for math. Now more than ever, it’s exactly what we need.

Julia Prise
Geometry, Algebra 2, College Algebra Teacher
Norman High School


Writing in the Math Classroom?! A Guided Inquiry Reflection

I remember the first day of my first Guided Inquiry Unit. I told my Algebra 2 students (a mixture of Sophomore-Seniors in high school) that we were going to try something a little different. I asked them to keep an open mind throughout the process. I explained that I was nervous about this unit, but asked for their support because I believed this unit would be of great interest to them. They nodded along, smiled, and promised to try their best.

Then, I asked them to complete their first journal prompt. In math class. Oh, the audacity. I can still see the eye rolling. One student actually muttered, “Ummm, Mrs. Prise, I have English next hour, not now.” I put on my best ‘fake it until you make it’ face and put up the journal timer.

I remember this day not because of the anxiety or the eye rolling of annoyed teens, but instead because it was the day that I learned something truly incredible – writing in math class allowed me to converse with and understand students in a way I never thought possible. Throughout the unit, students who never spoke in class wrote vivid reflections, and I had the opportunity to write back and continue our conversation. I was able to judge student’s understanding quickly, without having to have them complete a typical assessment. I gained insight on what my students appreciated about the GI unit, and what they would recommend I change. Most importantly, I understood what my students were thinking.

When the Guided Inquiry unit ended, both my students and I were sad that the journaling was over. It was back to goal quizzes, homework, and exams. As the days went on, I felt myself using various GI ideas to make my content more engaging and applicable to the real world. But, there was still a hole where the journaling had been.

I’m thrilled to say that in August, each student will keep a composition notebook in my classroom, and we will journal at least twice a week. Sometimes, the prompts will be used as a checkpoint for me to see what students understand and what students are struggling with. Other times, it will be used to check vocab comprehension. Finally, sometimes, the journal prompts will ask a goofy ‘would you rather’ question, so that I can honor and value my students as individuals. I can see them as more than just math students, but as people who deserve a cheerleader in their corner. Whether their journal entries are excited, happy, lonely, or angry, they will know their math teacher is there to help with whatever they need. I may not be able to complete every unit in a true Guided Inquiry manner, but that doesn’t mean I can’t improve my practice with its aspects and ideas.

Still think writing in journals is just something for the English classroom? Think again! I’m going to turn all my student’s ideas about math class upside down, and I’ve never been more anxious, or more excited.

Julia Prise
Geometry, Algebra 2, College Algebra Teacher
Norman High School

My Mathematical Journey to Guided Inquiry

As a high school math teacher, my overarching goal every year is to nurture a unique group of mathematically literate students. In today’s society, we are surrounded with numbers, statistics, and figures, and my goal as an educator is to create critical consumers of mathematics. In order to engage my students in this kind of thinking, they must be engaged and excited about mathematics. I am lucky enough to teach at Norman High School, where engagement is always on the forefront of classroom conversations. Last year, I had the privilege of attending a Guided Inquiry Training, and my eyes were immediately opened to a new, effective way in which to engage and interest my high school students. Guided Inquiry has given me, as an educator, the means to involve my students in mathematics while engaging them in interesting topics. Students can study math, something of interest to them, and become critical consumers of research and mathematics in one large swoop. I have completed two Guided Inquiry Units in Geometry and Algebra 2, and each project has impressed and surprised me more and more each time. My students have overwhelmingly enjoyed the Guided Inquiry process, journaling to me about their appreciation for individual choice, real life applications, and an overall change from traditional mathematics teaching. As I approach my fifth year in the classroom, my mind is already racing with Guided Inquiry ideas for my students to explore. I have the unique privilege to engage students in mathematics, and my students deserve nothing less than the best. Guided Inquiry has given me the opportunity to involve my students in research, data, and most importantly, engaging mathematical content.


Julia Prise
Geometry, Algebra 2, College Algebra Teacher
Norman High School

Gr.6 Science Inquiry

Hi! This is the last post for Brian Shin and Michael Alford. We have two previous posts, the last one can be found here.

Our students in gr.6 had just come up with their inquiry questions and were excited to delve deep.


This leads us to the Gather phase.

At this point a research rubric was introduced, outlining how many words and the type of visuals that should be included; also, to describe problems with researching their question in relation to scientific inquiry (for example, the distances of our universe makes inquiry more difficult); and to formulate a new “I Wonder” question manifested from their research that promotes further inquiry (but won’t be answered).

The boys now began their focused research to answer their Inquiry. They had to use a mix of sources including the cart of books, youtube videos, online websites, and podcasts. What they were to create with their research findings was left a mystery…

Impressions: Multiple reminders were absolutely necessary in addition to the initial review of the research rubric. You know 11 year old boys – once they get going it is as if they grow ‘blinders’! Teacher feedback in the form of check-ins at an individual level was helpful. However, we needed to keep in mind that Inquiry should avoid continuous ‘hand-holding’. A certain amount of autonomy fosters ownership and accountability.


A few classes were given to finish their research, and with their findings they were introduced to the next phase: Create.

Themed topics were announced and posted on the walls of the classroom. Some themes were: Black holes and dark matter, Space technology, Stars & Nebulae, Planet colonization including travel…etc..
The students then moved to the posted themes according to their own inquiry topic and groups were formed. If one grouping was too large then it would be split up.

Two options were outlined to the groupings for what they had to ‘create’:

  • make a website organized to display each boy’s Inquiry through page links.
  • make a collage of individual student infographics (using Pictochart or Canva) and place together collectively on a display board.

Impressions: Creating a website seemed to be the harder choice. They could use Wix, Weebly, or Google Sites. Some groups started to design a website but decided to switch to infographics after a period because of website creation difficulties. The infographics looked wonderful displayed together but due to time constraint creative license was limited. Ultimately, the inquiry process provided students with a learning tool that allowed for the generation of focused questions and deeper understanding. Bonus: this was all about their unique individual interests!

Pictochart or Canva infographics










Part of a website presentation


Some student inquiry questions are shown again below, but with their new ‘I wonder’ question to promote further inquiry for another time…

“Why can time slow down when you near a black hole?” – “I wonder how astronomers can test Einstein’s General Theory of Relativity?”

“How can we use the gravitational pull of a black hole to our advantage when travelling through space?” – “I wonder if the mass or size of a black hole affects the penrose process?”

“What is the process that creates energy for stars and how might humans use it as an energy source?” – “I wonder if nuclear fusion will ever be a main energy source for humans?”

“How might we create new space technology that is more advanced and doesn’t need fuel?” – “I wonder why fuel is one of the only things we have figured out to use that generates enough force to leave earth?”

“How can the nano craft of the project ‘Breakthrough Starshot’ withstand a force of 10,000 g’s?” – “I wonder how will the starshot company predict where exactly Proxima B will be in 20 years?”

“Why can’t we see dark matter? – “I wonder why the universe is predicted to collapse on itself?”



The Share phase

Our intention was for a gallery walk/show & tell, but alas time ran out. Therefore we have come up with our own “I wonder” question about this process: “We wonder how can students present a succinct, meaningful ‘take away’ regarding the entire process and what they learned?”


Thank you for reading our posts! We hope you gleaned some idea(s) from them. Good luck with your GID project!

Gr. 6 Science Inquiry

Hello again! Here is the second post of Brian Shin’s and Michael Alford’s gr.6 science inquiry. If you have not read the first post for an introduction, click here.

We continue now at the Explore phase.

In the book, Guided Inquiry Design, it is noted that the intention of this phase is to expose the students to a wide variety of sources where the focus is to skim over many topics and write down what is interesting to them. It is important to emphasize to them that this is not a search for as much information on one topic as they can gather. This last word is the confusion. The Explore phase is not the Gather phase where a topic has already been chosen.

We introduced the graphic organizers that would be needed for this phase: First, an Inquiry Log which keeps track of source names, and ranks how important or interesting the information in them is to the student. The second is a Stop and Jot form which allows the students to briefly write really interesting ideas from a particular source (going a bit deeper!)Both these graphic organizers are found in Guided Inquiry Design.

The sources that we made available to the students were: a trolley of library books, prepared for us by the librarian, a podcast website called ‘Starspot’, the website, and Youtube videos.

Luckily, we have many up to date books including multiple copies!


By the end of a couple of classes, we asked the boys to do a mini-assignment. They were to review the following:
1. Inquiry Journal video notes, and any other important journal entries.
2. Their “I wonder” questions from your shared Inquiry Circle Google slideshows.
3. Their notes from the “Gallery Walk” – “I see, I think I know, and I wonder”.

After review they must answer the following two questions and submit via our online school platform ‘Canvas’:
* What do you want to know more about?
* Which sources do you want to spend a little more time with? Explain.

Impressions: boys who had great ideas on topics and were previously engaged really flourished; but the boys who struggle with developing ideas and questions on their own had more challenges. We found sharing questions as a class after one session helpful to those boys. The Inquiry log and Stop and Jot forms are very helpful tools to organize immediate thoughts and research notes on paper. It is a nice mix of digital use with pencil and paper.


Exciting! Now for the development of their Inquiry question in the Identify Phase.

We introduced this Inquiry Chart from the book, Guided Inquiry Design; it has been changed a little visually, but the content remains the same.

Step by step development of an Inquiry question


Using a highlighter to focus on the most important ideas after reviewing all work to this point is helpful. Making more questions from these ideas is essential. Providing more graphic organizers to list these highlighted ideas scaffolds many students who struggle with visually organizing work.

Used as many of these as needed


From their collection of ideas and questions, the boys had to sort them into common themes which we called ‘clusters’.

Similar questions or ideas put into a cluster


Then from the cluster they would develop an Inquiry question. The boys could develop two or three clusters and Inquiry questions, but had to choose only one to investigate.

Here are some of their examples:

“Why can time slow down when you near a black hole?”

“How can we use the gravitational pull of a black hole to our advantage when travelling through space?”

“What is the process that creates energy for stars and how might humans use it as an energy source?”

“How might we create new space technology that is more advanced and doesn’t need fuel?”

“How can the nano craft of the project ‘Breakthrough Starshot’ withstand a force of 10,000 g’s?”

“Why can’t we see dark matter?”

Impressions: Similar to the Explore phase outcomes, boys who have a natural ability to connect ideas and formulate new ones were fast to go “deep”. Other boys needed more teacher feedback and guidance but overall they still were able to find a personal connection at a deeper level. Wonderful job!

Tomorrow: Gather, Create, and Share!

Gr.6 Science Inquiry – The Universe

Good day! Let’s start by introducing ourselves: our names are Brian Shin and Michael Alford. We are gr.6 science teachers at St. George’s Junior School in Vancouver, British Columbia, Canada. Our school is an all boys school and has fully embraced the GID model for learning. It is exciting to share our Guided Inquiry Design (GID) experience! Let’s take you through the process!

A unit of study in the B.C. gr.6 science curriculum is ‘The Universe’. The “Big Idea” noted in the curriculum is “The solar system is part of the Milky Way, which is one of billions of galaxies.” With such a large scope of available topics of study, it is easy for students to choose one and research many facts on it. But here is the issue: they end up not really focusing on one key idea, or connecting the student with the content at a much deeper and meaningful level. Thus, the end result of their project is typically a broad, superficial summary. We wanted to change that!

Luckily, there is a great support network at our school to help. Our librarian and faculty have already exposed the boys to this wonderful process, so the steps and expectations were familiar to all learners. Moreover, Leslie Maniotes is incredibly helpful and always available! Her book, Guided Inquiry Design is the ultimate resource, with detailed examples.

Today and the next couple of posts we will provide an account of how we used GID to promote deeper learning and also to provide some reflection on the process; we will review each GID stage and then write some “impressions”.


In the beginning…Open Phase

We thought visual! Boys especially connect with good visuals to stir the imagination.
The hook was to watch the video “The Milky Way HD” by National Geographic(available online) and were provided with a link to finish at home if needed, depending on class time. The boys started a journal here to keep a record of interesting ideas that they felt impressed by.

Impressions: spectacular visual introduction of space; advanced presentation in terms of concepts, that left them excited and curious. Each boy was given a portfolio folder to be kept in class; they also created a google doc that was to be their personal ongoing Inquiry Journal (thank goodness for the automatic saving which is a feature of this program!). Video notes were made in their journal to keep a record of interesting ideas that they felt impressed by. These ideas were shared on post-it notes on the board at video’s end, and the start of next class. Lots to think about!



For us, the most time consuming phase of GID is the Immersion.

The students were now exposed to concepts that continue to build on ideas generated in the Open phase.
What a better way to start to do this than a field trip! The Vancouver Planetarium was an easy choice for sure! Lots of hands on, kinesthetic activities, plus the mind-blowing dome show. Lots to write about for highlights in their journals!

This is hot!

SO heavy!








For the following class lesson photos were posted at points around the classroom. This was a “Gallery Walk” where they held a graphic organizer with columns headed ‘I see’, ‘I think I know’, ‘I wonder’. Listening to tranquil space music streamed from Youtube, and in silence, they took a few minutes at each picture to write in their organizer. The pictures ranged from a Nebula, space technology, birth of stars, etc..Once they made their way through most or all of the gallery, they got into their newly created Inquiry Circles to share important thoughts about the top 2 or 3 intriguing pics for each Circle member. Their portfolio would contain all written materials such as this.

Gallery Walk pic

Gallery walk activity









Building a base of background knowledge in addition to just highlighting key terms and definitions is critical in the Immersion phase. If researching this knowledge is too wide-ranging and individualized, students will not have a common platform to work from; selecting core principles for basic understanding is key. These concepts are chosen by the teacher so the class knowledge is uniform. We decided on an activity called a ‘Jigsaw’ which allows each member of the Inquiry Circle to become an expert on a general concept. Using an online resource such as the ESA – kids website is appropriate for accumulating a base of basic facts and understanding. Each member of the Circle would create a Google slideshow about the concept, and then ‘share’ his google slideshow with all Circle members. The Circle members would read all their ‘shared’ slideshow summaries (the Jigsaw is completed) and write an “I wonder” question in their journal for each. These questions add to the important ideas that the student is gathering. They would also have collected general background knowledge in the form of the slideshows for future reference.

Extreme environments and technology! How easy does it get to engage boys in learning! These topics were the focus for the rest of the Immerse phase. Educational sites offer videos such as the Apollo 13 mission that are actually quite riveting with real footage. Using guided questions and stopping the video frequently to discuss the extreme environment of space coupled with technological challenges, the students found the true story unbelievable! More reflection was written in their journals. Finally, a podcast site called ‘Starspot’ was introduced and one podcast on Electric solar sails was listened to, again with stop and start playing that allowed for discussion and understanding. The boys were asked to draw the technology based on what was described in the podcast. This was added to their portfolio.

Impressions: The longest phase of inquiry for sure! The field trip offered so many connections to topics and brought a tactile quality to the experience. Fun! The extreme environment of space came through clearly in the Apollo 13 video. The introduction of the inquiry circles promoted communication and reflection among peers. Having responsibility to share background knowledge with peers in the jigsaw activity was meaningful and promoted further inquiry through the I Wonder questions. A discussion around using a podcast as a source gave them insight into resource use. The pros of a podcast include the topic is very current and is presented by leading experts in the field. A downside for gr.6 can be the advanced nature of the presentation. Throughout the Immerse phase the boys got continuous feedback on their work to date from the teacher. Using an online school-wide platform called Canvas, we were able to give immediate feedback to their journals without using paper. Their portfolio that did include written handouts was monitored for completion at this stage.


Tomorrow – Explore and Identify!